Eastern Catholic Churches are not the same as Eastern Orthodox Churches. That further confuses the lay person.
I can appreciate that. In the ME, it is not uncommon for an Eastern Rite Catholic to marry someone from an Orthodox Church. They handle this in various ways. For example, in my parish, the women attend the church of the husband. As such, when major holidays like Christmas and Easter arrive, we often find Orthodox spouses attending our services on those feast days and vv. It all works out in the end.